Engaging structure for hand tool

An engaging structure comprising:

• a main body;
• the main body is an open wrench or an engaging portion of a hand tool;
• the main body includes a first side, a second side, a third side, and a fourth side;
• the first side is opposite to the second side;
• the first side, the third side, the fourth side, and the second side are arranged serially and annularly;
• the first side, the third side, the fourth side, and the second side of the main body are capable of contacting an inscribed hexagon;
• the hexagon is an equilateral hexagon;
• the hexagon has an axis;
• the hexagon has six sides each of which has a first length;
• a vertical line passes the axis in a two-dimensional plane;
• the hexagon has a first line, a second line, a third line, a fourth line, a first angled corner, a second angled corner, and a third angled corner;
• each of the first line, the second line, the third line, and the fourth line has a length equal to the first length;
• the first line aligns with the first side, the second line aligns with the second side, the third line aligns with the third side, and the fourth line aligns with the fourth side;
• the first side is provided with a first face and a first recess;
• the vertical line passes the first face;
• the first face has a planar shape;
• the first face is arranged asymmetrically relative to the vertical line;
• the first face extends to an opening of the main body;
• the first recess connects the third side;
• the first recess is provided with a first arcuate face and a second arcuate face;
• the first arcuate face connects the first face;
• the first arcuate face is tangent to the first face;
• the first arcuate face is tangent to the second arcuate face;
• the second arcuate face connects the third side;
• the first arcuate face has a radius having an integer value equal to that of a distance between the first line and the second line;
• if the integer value of the distance between the first line and the second line is 19 mm, the integer value of the radius of the first arcuate face is 19 mm;
• if the integer value of the distance between the first line and the second line is 18 mm, the integer value of the radius of the first arcuate face is 18 mm;
• the second side is provided with a second recess, a second face, and a third recess;
• the second recess is a single arcuate face;
• the vertical line passes the second face;
• the second face faces the first face;
• the second face has a planar shape;
• the second face is arranged asymmetrically relative to the vertical line;
• the third recess connects the fourth side;
• the second face is arranged between the second recess and the third recess;
• the third recess is a single arcuate face;
• the third recess is not tangent to the second face;
• the second recess has a radius more than that of the third recess;
• the fourth side is provided with a fourth recess;
• the fourth recess is close to the third recess;
• the fourth recess is a single arcuate face;
• the second recess has a radius more than that of the fourth recess;
• the fourth recess has a radius more than that of the third recess;
• a first angle is defined between the first side and the third side;
• the first angle is less than 120 degrees;
• a second angle is defined between the second side and the fourth side;
• the second angle is less than 120 degrees;
• the second angle is slightly more than the first angle;
• a fifth recess is defined between the third side and the fourth side;
• the fifth recess is arranged at a connection of the third side and the fourth side;
• the fifth recess includes a third arcuate face, a fourth arcuate face, and an intersection point;
• the third arcuate face connects the third side;
• the fourth arcuate face connects the fourth side;
• the third arcuate face is larger than the fourth arcuate face;
• and
• the intersection point is arranged at a connection of the third arcuate face and the third side.